强正则图的能量

设G是阶为n边数为m的简单图,λ1,λ2,…,λn是G的邻接矩阵的特征值,μ1,μ2,…,μn是G的拉普拉斯矩阵的特征值.图G的能量定义为E(G)=n∑i=1|λ1|,拉普拉斯能量LE(G)=n∑i=1|μ1-2m/n|.利用代数和图论的方法,得到了五一正则图的最大和最小能量,以及最大、最小拉普拉斯能量,并刻划了能量取到最值时对应的图的结构.

Energy of Strongly Regular Graph

Let G be a graph with,l vertices and,,l edges.Let λ1,λ2,…,λn be the eigenvalues of the adjacency matrix of G,and let μ1,μ2,…μn be the Laplacian matrix of G.The energy of G is defined as E(G)=n∑i=1|λi| ,the Laplacian energy LE(G)=n∑i=1|μ-2m/n|.In this paper,by algebra and graph methods,we obtain the maximum and minimum energy and Laplaeian energy of κ-regular graph G of order n when it form a strongly regular graph,and character the corresponding graph respectively.